Using properties of determinants prove the following questions. ∣∣

1.	Using properties of determinants prove the following questions. ∣∣∣∣∣αα2β+γββ2γ+αγγ2α+β∣∣∣∣∣=(β−γ)(γ−α)(α−β)(α+β+γ)
Answer» Using properties of determinants prove the following questions. $∣ ∣∣∣ ∣ \begin{matrix} α & α^{2} & β + γ β & β^{2} & γ + α γ & γ^{2} & α + β \end{matrix} ∣ ∣∣∣ ∣ = (β - γ) (γ - α) (α - β) (α + β + γ)$

Using properties of determinants prove the following questions. ∣∣∣∣∣αα2β+γββ2γ+αγγ2α+β∣∣∣∣∣=(β−γ)(γ−α)(α−β)(α+β+γ)

Answer»

Using properties of determinants prove the following questions.

$∣ ∣∣∣ ∣ \begin{matrix} α & α^{2} & β + γ β & β^{2} & γ + α γ & γ^{2} & α + β \end{matrix} ∣ ∣∣∣ ∣ = (β - γ) (γ - α) (α - β) (α + β + γ)$